It follows from the construction that $\omega(t)$ in the cohomology class $T^{\frac{2}{n}}2\pi c_{1}(\mathcal{O}(1)|_{\widehat{X}_{t}})$. Hence we get the volume

(7.148)

$$\int_{\widehat{X}_{t}}\frac{\omega(t)^{n}}{n!}=CT^{2}\sim(-\log|t|)^{-1}.$$

The above error estimate in particular gives

(7.149)

$$\int_{\widehat{X}_{t}}\Gamma_{t}\wedge\bar{\Gamma}_{t}\sim T^{2}\sim(-\log|t|)^{-1}.$$